This work is focused on extending the well-studied concept of stochastic orders on univariate random variables to multivariate random variables. One method for accomplishing this extension is to impose univariate stochastic orders on scalarizations of random vectors. Adopting this approach, the thesis provides several equivalent characterizations of the stochastic order for random vectors. The dissertation studies the role of the multivariate stochastic-order relations, especially when incorporated as a constraint in stochastic optimization problems. A new two-stage stochastic optimization model, which incorporates a multivariate convex-order relation, is introduced and analyzed and its numerical solution is addressed. Optimality conditions are established for the single- and two-stage optimization problems with multivariate stochastic-order constraints. Several numerical methods are developed for solving the optimization problems with particular multivariate order constraints: stochastic dominance of second order and the multivariate counterpart of the increasing convex order. Several applications of the proposed models to finance and management problems are presented in detail with a discussion of numerical results.
|Commitee:||Collardo, Ricardo, Florescu, Ionut, Gilman, Robert, Ruszczynski, Andrzej, Zabarankin, Michael|
|School:||Stevens Institute of Technology|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 76/12(E), Dissertation Abstracts International|
|Subjects:||Mathematics, Operations research|
|Keywords:||Numerical methods, Ordering constraints, Stochastic optimization|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be